1. Field of the Invention
This invention relates to an active matrix liquid crystal display panel of the structure wherein liquid crystal is held between transparent insulating substrates.
2. Description of the Related Art
An active matrix liquid crystal display panel (hereinafter referred to as AMLCD) wherein a thin film field effect transistor (hereinafter referred to as TFT) is used as a switching element for a pixel has a high picture quality and is utilized widely as a display device for a portable computer or a monitor for a desk top computer of the space saving type.
In recent years, in order to achieve a high quality of a liquid crystal display, a display method called in-plane switching mode which makes use of a transverse electric field in order to improve the visibility angle characteristic has been proposed (for example, Asia Display '95) (Prior Art 1).
According to the display method, a pixel electrode and an opposing electrode are formed in parallel to each other, and a voltage is applied between the pixel electrode and the opposing electrode to form a parallel electric field in a plane of a liquid crystal layer to vary the direction of the director of the liquid crystal thereby to control the amount of transmission light therethrough.
In the liquid crystal display system described above, since the director moves only in a direction substantially parallel to and in the plane of the liquid crystal layer, such a problem that, as the director rises out of the plane of the liquid crystal layer as in the TN (Twisted Nematic) mode, the relationship between the transmission light amount and the applied voltage exhibits a large difference whether the liquid crystal layer is viewed from the direction of the director or from the direction of a normal to the liquid crystal layer does not occur, and a display image which looks in a similar manner from whichever direction it is viewed can be obtained over a very wide visual angle.
FIG. 1 is a view showing a liquid crystal display system which is driven by a transverse electric field and exhibits a good display characteristic.
For the display system described above, several systems have been proposed depending upon the initial orientation condition of the liquid crystal layer and the manner of setting of polarizing plates. Of those systems, such a system as shown in FIG. 1 wherein a liquid layer is injected in the same direction on both substrates and, in the initial orientation condition, the directors are oriented uniformly in this direction while one of two polarizing plates between which the substrates are held and which form a cross nicol is oriented to the direction of the directors in the initial condition so that, when no voltage is applied, a black display is obtained, but when a voltage is applied, the directions of the directors are turned to obtain a white display, is considered advantageous in that the black level can stable be made low.
In the display mode of the display system described above, the transmission factor T of light coming in from the front is given in accordance with the turning angle φ of the directors based on the following expression:T=sin2(2Φ)·sin2(π·Δndeff/λ)  (1)
where deff is the effective value of the liquid crystal layer thickness which undergoes turning deformation when the liquid crystal directors are twist deformed while they are large at a central portion and are fixed at interfaces of the liquid crystal with the substrates, and is smaller than the actual liquid crystal layer thickness.
It has been experimentally confirmed that, for example, where a liquid crystal cell of 4.51 μm thick is formed and liquid crystal having a dielectric constant anisotropy Δn=0.067 is injected in the liquid crystal cell, if a transverse electric field is applied so as to induce a deformation corresponding to φ=45 degrees, the transmission factor exhibits a wavelength dependency as seen from the expression (1) and has a maximum value substantially at λ=550 nm. Conversely, from this, it is esteemed that deff=4.1 μm using the expression (1), and the transmission factor for any other wavelength substantially coincides with a value obtained by substituting deff=4.1 μm into the expression (1).
In this instance, between the representative wavelength 460 nm selected by a color filter of blue and the representative wavelength 610 nm selected by another color filter of red, the transmission factor given by the expression (1) varies within a range less than 10% the highest value thereof. However, even if a special process is not performed, a significantly coloring image does not look when the liquid crystal cell is viewed from the front. Where a higher color purity is required, transmission lights from the color filters of R, G and B can be balanced well by adjusting the transmission factors of the color filters or the spectrum of back light.
It is examined here that, when a transverse electric field is applied to turn the directors approximately by 45 degrees to provide a white display, a substrate is viewed obliquely from a direction perpendicular to the turned directors.
FIGS. 2(a) and 2(b) are views illustrating transmission of light through liquid crystal when it comes in obliquely, and wherein FIG. 2(a) is a view as viewed from an oblique direction with respect to a substrate and FIG. 2(b) is a view as viewed from a parallel direction to the substrate.
While the transmission factor of light passing obliquely through a liquid crystal cell is not precisely represented by the expression (1), it is essentially same in that the light passes through a cross nicol as a retardation is produced between an ordinary ray and an extraordinary ray when it passes through the liquid crystal. Accordingly,f=sin2(π·ΦnL/λ)  (2)
wherein deff of the second factor of the right side of the expression (1) is replaced with the optical path length L when a ray passes through the effectively turned liquid crystal layer, makes an important factor which dominates the intensity of the transmission light.
When the liquid crystal cell is viewed from the front, with green light corresponding to λ=550 nm, the transmission factor spectrum has a maximum value, and consequently,π·Δndeff/λ=π/2  (3)and the factor f in expression (2) is 1.
As seen from FIGS. 2(a) and 2(b), when the liquid crystal cell is viewed from a direction which is perpendicular to the directors and oblique to the substrate, the refractive index anisotropy Δn felt with transmission light is the difference in length between the major axis and the minor axis of an ellipse which corresponds to a section of a refractive index ellipsoid of revolution having a major axis in the direction of the directors of the liquid crystal when the refractive index ellipsoid of revolution is cut along a wave front of the ray. In this instance, since the wave front includes the major axis of the ellipsoid of revolution, the refractive index anisotropy Δn felt with the light is fixed irrespective of the inclination angle θ from the direction of a normal to the substrate. Accordingly, as the inclination angle θ increases, π·ΔnL/λ gradually increases from π/2, while the factor f given by the expression (2) decreases and, reflecting this, also the transmission factor T decreases.
With light of red corresponding to λ=610 nm,π·Δndeff/λ<π/2  (4)on the front, and the factor f is smaller than 1. From the same reason as in the case of λ=550 nm, as θ increases, π·ΔnL/λ increases, and after it becomes equal to π/2, it further increases exceeding π/2. In response to the increase, also the factor f becomes equal to 1 once, and thereafter decrease gradually.Consequently, also the transmission factor T reflects this and increases once and then decreases gradually.
On the other hand, with light of blue corresponding to λ=460 nm,π·Δndeff/λ>π/2  (5)on the front, and the factor f is smaller than 1. From the same reason as in the case of λ=550 nm, as θ increases, π·ΔnL/λ increases and is spaced farther from π/2. Consequently, f decreases farther from 1. Since the rate of increase of f when the optical path length L increases is given byδf/δL=(π·Δn/λ)·sin(2π·ΔnL/λ)  (6)as π·ΔnL/λ increases exceeding π/2, f decreases suddenly. Accordingly, it can be said that the decrease of f where λ=460 nm is more sudden than that when λ=550 nm, and also the transmission factor T decreases suddenly.
From the foregoing, since, as θ increases, blue light decreases most suddenly and green light decreases comparatively moderately whereas red light first increases and then decreases, although white light looks on the front, as θ increases, the light gradually appears coloring with red.
This can be confirmed more quantitatively by a simulation which is performed taking a deformation and an optical anisotropy of liquid crystal into consideration.
FIG. 3 is a diagram illustrating a relationship between the inclination angle and the transmission factor when, in order to display white, light comes into a substrate from a direction perpendicular to the liquid crystal directors and oblique to the substrate. It is to be noted that the axis of abscissa indicates the inclination angle θ and the axis of ordinate indicates a result of calculation of the transmission factor normalized with the transmission factor on the front.
As seen from FIG. 3, as θ increases, the transmission factor generally decreases, and above all, it can be seen that the transmission factor for blue decreases most rapidly.
FIG. 4 is a diagram illustrating a relationship between the inclination angle and the transmission factor when, in order to display white, light comes into a substrate from a direction same as the direction of the liquid crystal directors and oblique to the substrate.
As seen in FIG. 4, when the line of sight is gradually inclined to the same direction as that of the directors in a white display, if a similar simulation is performed, it can be seen that red light conversely exhibits the most significant attenuation.
The phenomena described above occur quite similarly with an actual color liquid crystal display panel on which color filters are provided. In fact, it has been confirmed that, when a color liquid crystal panel produced in the same conditions as those of the liquid crystal cell described above is viewed from an oblique direction, it looks coloring.
As described above, with an active matrix liquid crystal display apparatus which is constructed using a transverse electric field, although a good display characteristic is obtained over an angle of visibility wider than that of a conventional TN mode, when viewed from an oblique direction, depending upon the direction, a display image looks coloring significantly. If such coloring occurs, then when image data of full colors are to be displayed, the image of the original picture is deteriorated remarkably.
On the other hand, methods of forming, in a liquid crystal display panel having color filters, liquid layers for the colors of the color filters with different layer thicknesses are disclosed in Japanese Patent Laid-Open Application No. Showa 60-159831 (Prior Art 2) and Japanese Patent Laid-Open Application No. Showa 60-159823 (Prior Art 3). The methods propose a display system wherein liquid crystal is held between two glass substrates and a voltage is applied between transparent electrodes on the opposite sides of the liquid crystal to vary the alignment of the liquid crystal layer, above all, of a liquid crystal display apparatus of the twisted nematic (TN) mode, and besides relates to a method of optimizing the characteristic when the liquid crystal display apparatus is viewed from the front. Those methods are quite different in structure, purpose and principle from the present invention which has been made to suppress coloring which occurs upon oblique light incidence in a transverse electric field display system which has a picture quality much higher than that of the TN system as hereinafter described.
Different methods are proposed in Japanese Patent Laid-Open Application No. Heisei 1-277283 (Prior Art 4) and Japanese Patent Laid-Open Application No. Heisei 6-34777 (Prior Art 5) wherein the thickness of a liquid crystal layer is optimized for individual colors in order to improve the characteristic on the front in simple matrix driving. Similarly, however, the methods are essentially different from the present invention.
Further different techniques are proposed in Japanese Patent Laid-Open Application No. Showa 60-159827 (Prior Art 6), Japanese Patent Laid-Open Application No. Heisei 2-211423 (Prior Art 7) and Japanese Patent Laid-Open Application No. Heisei 7-104303 (Prior Art 8) wherein liquid crystal layers are formed with different thicknesses for the colors of color filters. However, they relate to a structure and a production method proposed to optimize the front characteristic of the TN mode and are essentially different from the present invention.
As described above, with an active matrix liquid crystal display apparatus which is constructed using a transverse electric field, while a good display characteristic is obtained over a wider angle of visibility than that of the conventional TN system, there is a problem in that, when viewed from an oblique direction, significant coloring appears depending upon the direction, and consequently, when image data such as, for example, a photograph are to be handled, the image of the original picture is deteriorated very much.
Again, in recent years, in order to achieve a higher quality of a liquid display, a displaying method called in-plane switching mode (hereinafter referred to simply as “IPS”) which makes use of a transverse electric field in order to improve the visibility angle characteristic has been proposed. An example was published in “Asia Display '95 ” held in Oct. 10 to 18, 1995 and is disclosed in “Principles and Characteristics of Electro-Optical Behaviourwith In-Plane SwitchingMode”, a Collection of Drafts for the Asia Display '95. The liquid crystal panel disclosed is constructed such that, as shown in FIG. 5, a linear pixel electrode 71 and a linear opposing electrode 72 are formed in parallel to each other on one of a pair of substrates 70 between which a liquid crystal layer is held, but no electrode is formed on the other substrate. A pair of polarizing plates 73 and 74 are formed on the outer sides of the substrates 70 and have polarization axes 75 and 76 extending perpendicularly to each other. In other words, the polarizing plates 73 and 74 have a positional relationship of a cross nicol to each other. A voltage is applied between the pixel electrode 71 and the opposing electrode 72 to produce a transverse electric field 77 parallel to the plane of the liquid crystal layer, whereupon the directions of the directors of liquid crystal molecules are varied from an initial orientation direction 78 thereby to control transmission light through the liquid crystal layer.
In the twisted nematic mode (hereinafter referred to simply as “TN”), since liquid crystal molecules rise three-dimensionally from the plane of the liquid crystal layer, the manner in which the liquid crystal layer looks is different whether it is viewed in a direction parallel to the directors of rising liquid crystal molecules or in another direction normal to the liquid crystal layer. Further, there is a problem in that, when the liquid crystal display panel is viewed from an oblique direction, the relationship between the applied voltage and the transmission light amount is different very much. More particularly, as seen from a voltage-transmission factor characteristic illustrated as an example in FIG. 6, where a liquid crystal display panel of the TN mode is viewed from the front, the characteristic makes a monotonously decreasing curve wherein the transmission factor decreases as the applied voltage increases after it exceeds 2 V. However, where the liquid crystal display panel of the TN mode is viewed from an oblique direction, the characteristic makes such a complicated curve having external values that, as the applied voltage increases, the transmission factor decreases once until it comes to 0 at the voltage of 2 V, but as the voltage thereafter increases, the transmission factor increases until it decreases again after the voltage exceeds approximately 3 V. Accordingly, if the driving voltage is set based on the voltage-transmission factor characteristic when the liquid crystal display panel is viewed from the front, then when the liquid crystal display panel is viewed from an oblique direction, there is the possibility that gradation reversal may occur such that a white displaying portion looks black or a black displaying portion becomes whitish. After all, normally the display of the liquid crystal display panel of the TN mode is visually observed correctly and can be used only within the range of the angle of visibility of 40 degrees in the leftward and rightward directions, 15 degrees in the upward direction and 5 degrees in the downward direction. Naturally, the upward, downward, leftward and rightward directions can be modified by the installation of the liquid crystal display panel.
On the other hand, the in-plane switch (IPS) system is advantageous in that, since liquid crystal molecules move only in directions substantially parallel to the plane of the liquid crystal layer (two-dimensionally), a substantially similar image can be obtained as viewed from an angle of visibility wider than that of the TN system. Particularly, the IPS system can be used within the range of an angle of visibility of 40 degrees in the upward, downward, leftward and rightward directions.
As apparatus of the IPS system, various liquid crystal display panels have been proposed which have various constructions depending upon the initial orientation condition of the liquid crystal layer and the manner of setting of polarizing plates. In the example of FIG. 5 described above, the liquid crystal layer is processed by interface orientation processing in the same direction for the two substrates and the polarization axis of one of the two polarizing plates extends in parallel to the orientation direction. This liquid crystal display panel allows a stabilized black display since, in the initial orientation condition, the directors of liquid crystal molecules are oriented uniformly in the direction of the interface orientation processing and black is displayed when no voltage is applied, but when a voltage is applied, the directors are turned so that white is displayed.
As described above, with an active matrix liquid crystal display panel of the IPS system which makes use of a transverse electric field, a good display characteristic can be obtained over an angle of visibility wider than that of the conventional TN system. However, also the active matrix liquid crystal display panel of the IPS sometimes suffers from gradation reversal depending upon the angle at which the active matrix liquid crystal display panel is viewed. Where gradation reversal occurs in this manner, there is a problem that, if an image principally of a black color such as hair of a human being is displayed, then a good image cannot be obtained when it is viewed from an oblique direction to the active matrix liquid crystal display panel.
This problem is described in more detail below. First, the transmission factor where the liquid crystal layer is omitted and only two polarizing plates are disposed in a positional relationship of a cross nicol to each other. It is to be noted that, of the two polarizing plates, that one which is disposed on the light incoming side is a polarizer, and the other one which is disposed on the light outgoing side is an analyzer.
In FIG. 7, the unit vector in the absorption axis direction of the polarizer is represented by e1, the unit vector in the absorption axis direction of the analyzer by e2, and the unit vector in the substrate normal direction by e3. Those unit vectors extend perpendicularly to each other. The unit vector in the direction of a ray when it passes through the polarizer is represented by k. Where the angle between the vector k and the substrate normal line is represented by a zenithal angle α and the angle between a projection of the vector k on the plane of a substrate and the vector e1 is represented by an azimuth φ, the vector k is represented ask=sin αcos φ·e1+sin α·sin φ·e2+cos α·e3  (7)
Light when it passes through the polarizer can be considered to be composed of a polarized light component of the (e1 x k) direction and another polarized light component of the ((e1 x k) x k) direction. It is to be noted that the symbol “x” between vectors represents the product of the vectors. Since the former is normal to the absorption axis e1, theoretically it is not absorbed. On the other hand, the latter is absorbed by the polarizer. If the product of the absorption coefficient and the film thickness of the polarizer is sufficiently large, then the latter polarized light component is 0 after the light passes through the polarizer.
The refractive indices of the two polarizing plates (polarizer and analyzer) are substantially equal to each other and the directions of the ray when it passes through the analyzer is equal to k, when the ray passes through the analyzer, the light is separated into a polarized light component of the (e2 x k) direction and another polarized light component of the ((e2 x k) x k) direction. The latter polarized light component is absorbed substantially completely during passage through the analyzer while only the former polarized light component remains. Accordingly, if the influence of reflection at the surface of the glass and so forth is ignored, then the transmission factor T is represented as                     T        =                              {                                          1                                  2                                            ·                                                                    e                    1                                    ×                  k                                                                                                              e                      1                                        ×                    k                                                                                ·                                                                    e                    2                                    ×                  k                                                                                                              e                      2                                        ×                    k                                                                                          }                    2                                    (        8        )            
By representing the expression (8) using α and φ,                     T        =                              1            2                    ·                                                    sin                4                            ⁢                              α                ·                                  sin                  2                                            ⁢                              ϕ                ·                                  cos                  2                                            ⁢              ϕ                                                                        sin                  4                                ⁢                                  α                  ·                                      sin                    2                                                  ⁢                                  ϕ                  ·                                      cos                    2                                                  ⁢                ϕ                            +                                                cos                  2                                ⁢                α                                                                        (        9        )            is obtained.
When light comes in from an azimuth equal to the direction of the absorption axis of one of the polarizing plates such as where the azimuth φ is 0 degree or 90 degrees, the transmission factor T is 0 from the expression (8). In other words, similarly to the case wherein light comes in from the front, the light does not pass due to the action of the polarizing plates which are at the positions of a cross nicol.
On the other hand, where the azimuth φ=45 degrees, that is, where the azimuth φ defines 45 degrees with respect to each of the absorption axes of the two polarizing plates, as the zenithal angle α increases, the transmission factor increases. Where the refractive index of the polarizer is 1.5, since the refractive index of the air is approximately equal to 1, the highest value of sin α is approximately 1/1.5. If this is substituted into the expression (9) to calculate it, the resulting transmission factor is approximately 7%. Actually, however, since reflection occurs at the interface between each of the polarizing plates and the air due to the difference in refractive index between them, if a simulation is performed taking the reflection into consideration, then the relationship between the inclination angle (zenithal angle) α of the ray in the air with respect to a normal to the substrate and the transmission factor is such as indicated by a curve 1 of FIG. 8.
Next, another case is described wherein liquid crystal having a positive dielectric constant anisotropy and having a refractive index anisotropy with no=1.45 and Δn=0.067 is held between two polarizing plates such that the directors are oriented in the same direction (α=90 degrees and φ=0 degree) as that of the absorption axis of the analyzer. Light having passed through the polarizer advances, in the liquid crystal, in a direction a little different from the direction of the light in the polarizer. As a result, the linearly polarized light polarized uniformly when it passes through the polarizer becomes elliptically polarized light after it passes through the liquid crystal. Consequently, the transmission factor is different from that where the liquid crystal is absent. The relationship between the zenithal angle α and the transmission factor when light comes in from the direction of the azimuth φ=45 degrees is indicated by a curve 2 in FIG. 8. In this instance, the transmission factor is rather higher than that (curve 1) where only the polarizing plates of a cross nicol are arranged while no liquid crystal layer is present.
On each substrate interface, the liquid crystal directors do not extend completely parallel to the plane of the substrate but normally rise by approximately 1 to 10 degrees with respect to the plane of the substrate. This angle is a pretilt angle. Usually, since, in order to orient liquid crystal with a higher degree of stability, interface orientation processing such as rubbing is performed such that the orientation directions of liquid crystal molecules may extend in parallel to each other in the proximity of each interface, the liquid crystal molecules are inclined by a fixed angle with respect to the plane of the substrate substantially in all regions. Where an orientation film for industrial use which is high in stability is employed, generally the pretilt angle is approximately 3 degrees.
The relationship between the zenithal angle α and the transmission factor where the pretilt angle is 3 degrees and light comes in from the direction of the azimuth φ=45 degrees is such as indicated by a curve 3 in FIG. 8. Further, the relationship between the zenithal angle α and the transmission factor where the pretilt angle is −3 degrees and light comes in from the direction of the azimuths φ=45 degrees is such as indicated by a curve 4 in FIG. 8. It is to be noted that the pretilt angle when the liquid crystal rises in the same direction as the vector e1 is taken as positive, and the pretilt angle when the liquid crystal rises in the opposite direction to the vector e1 is taken as negative. Particularly where the liquid crystal rises in the same direction as the vector e1 (where the pretilt angle is positive), the transmission factor has a value approximately twice that in the case where only the polarizing plates are present (no liquid crystal is present).
Since the curves 1 to 4 of FIG. 8 exhibit comparison among black display conditions when no electric field is applied to the liquid crystal as described above, preferably the transmission factor is as low as possible. However, the curve 3 has a very high transmission factor comparing with the curves 1, 2 and 4. Therefore, the case of the curve 3, that is, the case wherein the pretilt angle is 3 degrees, is described in more detail.
While description has been given above of the case wherein no electric field is applied to the liquid crystal, if a transverse electric field is applied to the electric field to turn the directors in the plane of the liquid crystal layer, then the transmission factor increases. According to a simulation by calculation, the transmission factor when the potential difference between a pixel electrode and a common electrode is 3 V is approximately 2.4%, and the transmission factor when the potential difference is 3.5 V is approximately 6.3%. FIG. 9 shows graphs obtained by plotting results of calculation of the transmission factor variation when the zenithal angle α is varied while the pretilt angle is 3 degrees and azimuth φ=45 degrees. When no electric field is applied (V=0 V), the graph is same as the curve 3 of FIG. 8 described hereinabove. When an electric field is applied, a result is obtained that, as the zenithal angle α increases, the transmission decreases, and the curve for V=3.0 V crosses in the proximity of the zenithal angle α=37 degrees, but the curve for V=3.5 V crosses in the proximity of the zenithal angle α=50 degrees, with the curve for V=0 V when no electric field is applied (when the liquid crystal is in the initial orientation condition), and thereafter the transmission factor and the brightness are reversed. In other words, when the potential difference is 3.0 V, where the zenithal angle α is smaller than 37 degrees, the transmission factor is higher where a voltage is applied than where no voltage is applied, but where the zenithal angle α exceeds 37 degrees, the transmission factor is lower where a voltage is applied than where no voltage is applied. Accordingly, where the zenithal angle α exceeds 37 degrees, a voltage applied portion becomes rather black while a no-voltage applied portion becomes rather white, and so-called gradation reversal wherein the black and white displays are reversed to ordinary black and white displays occurs. It is to be noted that, since the transmission factors at a voltage applied portion and a no-voltage applied portion are not much different from each other in the proximity of the zenithal angle α=37 degrees, the contrast is small and the display image cannot be observed well. Similarly, where the potential difference is 3.5 V, gradation reversal wherein the transmission factors between a voltage applied portion and a no-voltage applied portion are reversed to each other occurs around the zenithal angle α of 50 degrees.
The phenomenon of gradation reversal described above is observed also with actual devices. Although depending upon the relationship between the pretilt angle of the liquid crystal and the directions of absorption axes of the polarizing plates, depending upon a direction in which the active matrix liquid crystal display panel is viewed, gradation reversal sometimes occurs when the display panel is viewed from an angle of 40 degrees.
In this manner, with the active matrix liquid crystal display apparatus of the IPS system which is constructed using a transverse electric field, while a good display characteristic is obtained over a wider angle of visibility than that of the conventional TN system, there is a problem in that, depending upon a direction in which the display apparatus is viewed, gradation reversal occurs, and particularly where a display which includes much black is viewed from an oblique direction, a good image cannot be obtained.
As described above, when a substrate is viewed obliquely from a direction of, for example, 45 degrees with respect to the polarization axes of two polarizing plates which are in a positional relationship of a cross nicol, a white floating phenomenon occurs because a phenomenon that, at a portion at which no voltage is applied, transmission light from one of the polarizing plates is absorbed but not completely by the other polarizing plate occurs. Further, since liquid crystal having a refractive index anisotropy is held between the two polarizing plates, the degree of the white floating phenomenon of the liquid crystal display panel is not fixed-because light (linearly polarized light) having passed through one of the polarizing plates undergoes double refraction so that it is changed into elliptically polarized light, which enters the other polarizing plate. Where the directors of the liquid crystal on the plane of the substrate are oriented such that projections thereof extend in parallel to the polarization axis of one of the polarizing plates and they define a fixed pretilt angle with respect to the plane of the substrate as in an ordinary liquid crystal display which makes use of a transverse electric field, as seen in FIG. 8, the white floating intensity becomes very high depending upon the rising direction of the liquid crystal. if the white floating is intensified in this manner, then gradation reversal sometimes occurs at a low zenithal angle as seen in FIG. 9.